That is confusing since closed-weight models (the models, not the applications using the models) also can't track outputs. It would be weird if the rules applied to the model and not the application because then it literally only applies to open-weight models since the closed-weight models are, by definition, never released to the public.

Trying to understand the rules but it doesn't seem to make a clear distinction between these things. I assume that they are intending the applications that use the models, not the models.

Of course they can. Lets assume you are using such a model in your product, this now makes tracking its output your responsibility. It is really no different from the way you would use an open source library.